2. Appropriate Use . . .

Today's seminar will cover the following topics:
  • Using Technology Appropriately
  • An Example From MTH 121
  • A MTH 121 Project
  • An Example From MTH 122
  • A MTH 122 Project
  • Math Teacher Link
  • Questions & Answers?

Using Technology Appropriately

Mathematica was released in 1988 and had a profound effect on the way computers were used in technical fields. I experienced this first hand, mainly because I was interested in solving numerically difficult problems that required vast amounts of code to do---I in fact had to write programming routines for simple arithmetic, and then rely upon Newton’s method to solve difficult equations. Yes, calculators were available, and I had two graphic calculators, but they were really quite primitive in 1988. Although there were other computer algebra systems available, Mathematica basically leap out to an audience waiting for such a product. I was certainly in that audience and quickly purchased a copy of Mathematica 1.0 for my dual floppy 1 MB Mac SE.

Some said that Mathematica marked the beginning of modern technical computing. Although not first to market, Mathematica created a single product that could handle many aspects of technical computing. Its use has expanded over the years and it remains one of the most important computer algebra systems ever. As educators we not only need to encourage our students to explore tools that will aid them now, but also allow them to prosper in their professional lives.

Keep in mind that Mathematica is used by all of the top Fortune 50 companies, all of the world’s 50 largest universities, and all of the 15 major departments of the U.S. government. So please consider that we need to get our students ready for a future that involves using Mathematica.

Like any technology, its use must be appropriate. However, just getting students started will be your greatest challenge. You'll certainly need to create teaching moments that shake the students into understanding that not all problems are pen-and-paper solvable. So today's talk will be about created teachable moments in my MTH 121 and 122 classes.

An Example From MTH 121

Taking derivates of many functions is really too easy, and I do work through a plethora of examples to drive the point across. Algebra skills in a majority of our students is quite poor, and I spend weeks on emphasizing that simple problems should be done by hand. However, I do lead into problems that require algebraic mettle well beyond what my students are capable of doing. And this is where I start to discuss using heavy tools (Mathematica).
  • I'll briefly address how my lecture (this is an old example that I am no longer using) notes lead to introducing Mathematica.
  • I occasionally update students electronically, and I try to keep it brief. For example, after the above lecture was given, I post a video that hopefully clarifies my lectures. What's great about posting videos is that students can watch again-and-again if they need to.
  • I certainly try my best to get students to attend my lectures, but as many of us know, attendance (lateness aside) at ECC is abysmal and has a great impact on our educational outcomes. Many of the videos posted are a direct outcome from my lectures. In this video---posted immediately after problem was discussed in class---I address the issue of using Mathematica to solve a word problem that caused much confusion in class. Keep in mind though, that students who don't attend probably won't watch the videos either. So please try to create resources that benefit students who attend your classes. What you do should relate to class content!

A MTH 121 Project

The students were informed about using Mathematica in prior lectures, and then I give them a project to work on where they are encouraged to use Mathematica (or other CAS software) to complete the work.
  • Actual assignment given to students.
  • Actual assignment key given to students after grades are recorded.
  • A video shared with students indicating what I wanted them to do.

An Example From MTH 122

While lecturing---really more like entertaining my students---I often come to realize that those under my spell aren't really listening, let alone understanding, what I am presenting. Of particular note is while reviewing MTH 121 with my MTH 122 students, is a lecture (this is no longer being used) on differential equations. I repeatedly inform my students that I don't actually draw my own direction fields, but that both the book and standardized calculus assessments require it. Even Euler's method is required in the both the textbook and standardized assessments. Students look concerned, but I do assure them that I am not going to require them to draw a direction field, and that I will provide them if it's helpful in solving a problem. However, I try to slowly pace my students into seeing technology as an aid, and here's two examples related to the lecture on differential equations:
  • Video of graphing direction fields and Euler's solution.
  • Using Excel to compute Euler's method.
As we proceed forward, invariable someone asks about Mathematica. Typically I'm asked, "Is there a way I can get a license or installation password for Mathematica 7 on my laptop from the school?" And here's a typical group reply that I give early in the semester:
One student in our class asked about Mathematica, but at some point during the semester everyone needs to get exposed to Mathematica. Sooner the better, just poke around ECC's computer labs and look for the Mathematica program. Here's a brief video to get you started.
Since my MTH 122 students are more advanced, I tend to post less direct information about using Mathematica, but I do post videos that will nudge students into using/learning Mathematica.

A MTH 122 Project

I trudge through numerical methods of integration, and actually do some calculations in class. Watching "paint dry" is more like it, and I think at this level that methods should be taught, but the tedium of computation is best left to a machine. Here's an example assignment for numerical integration. Then later in the semester, I actually give more screencasts related to using Mathematica.
And students are asked to use Mathematica on occasion.
  • Please visit my MTH 122 website for full course notes. These notes include Mathematica example code and problems.

Math Teacher Link

Okay, if you're really motivated, you might want to consider some formal training from the University of Illinois at Urbana-Champaign. They have a course for mathematics teachers interested in using Mathematica as a teaching tool. Here's the blurb from their website:
Calculus & Mathematica for Mathematics Teachers Calculus & Mathematica is a university credit, modern calculus course based on an interactive, electronic text. It is currently offered on campus at a number of universities, and by distance education at many high schools. This module introduces teachers to the content and pedagogy of the Calculus&Mathematica course. This module is suitable for any mathematics teacher interested in teaching, or simply learning more about, the Calculus&Mathematica course. Credit: 1 grad. sem. hr. or 3 CEUs.

Questions & Answers?

Feel free to ask questions. Even if you did not attend the live seminar, please feel free to leave a comment and I'll do my best to address your questions or concerns.


Ron Bannon said...

You can also stop by my office, room 2210, and have a one-on-one with me if you prefer. I know how difficult it can be to make time for a seminar.

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